In this paper, we explore the use of dynamic geometry software (DGS) as a medium for
changing student and teacher interactions (and attitudes) with functions. We o er three
examples of sketches that may be used to encourage students to build their own functions.
Moreover, we share a strategy for developing additional sketches, namely our three-step
MTA process (Measure - Trace - Algebratize). Note that these steps roughly correspond
to concrete, iconic, and symbolic levels of representation proposed by Bruner (1960; 1966).
As our examples illustrate, the MTA approach provides students with opportunities to
explore and construct remarkably non-standard functions - often beautiful, unexpected,
and thoroughly original.